There are several ways. One is to have financial need, the other is to have an outstanding academic record. You can look for federal pell grants as well.
Merit scholarships are provided based on grade point average. Other scholarships are based on need. However, there are many scholarships that are not school specific and can be applied anywhere.
You can achieve a scholarship to Princeton (or any other Ivy college), by applying and hoping that your grades are good enough to meet that school's requirements. Princeton is one of the best schools though, so it will be difficult.
There are institutional scholarships which are available directly through the school for certain achievements and many other programs. Other private organizations and businesses typically offer this type of financial assistance. You must fill out a FAFSA to be eligible for these. Ask the school guidance counselor for more information.